Is it permissible for a father to differentiate between his children in gifting, and if he does so, would the daughter be considered disobedient if she filed a lawsuit demanding justice? And is it permissible for a wife to excuse her husband from spending the night with her for the purpose of ensuring justice between wives?

Justice between wives is obligatory unless one of them waives some of her rights, such as overnight stay. If the first wife's waiver of her right to overnight stay for her co-wife is valid, then there is no sin upon the husband; otherwise, he must repent and seek forgiveness.

As for a father singling out some of his children for something over others, it is permissible if there is a legitimate شرعي reason. Otherwise, it is a matter of dispute, and the preponderant opinion is that it is forbidden.

It is advisable to try to convince the father to be just between his children with politeness and respect, and to involve family and relatives. If he accepts the advice, then so be it; otherwise, continue advising him gently.

However, taking the father to court is an act of disobedience (عقوق), because merely making a parent swear an oath is an act of disobedience.